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所在平台: Udemy |
课程主页: https://www.udemy.com/course/fourier-series-part-1-college-mathematics/
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课程名称：人工智能的傅里叶级数和变换基本理解 课程概述：欢迎参加本门关于傅里叶级数的课程。这是工程数学的一部分，由数学教育者和辅导员Suman Mathews讲授。Suman拥有数学双硕士学位，教授数学已有三十年，面向大学和高中学生。在这门课程中，您将学习分析数学的基本知识。课程将介绍欧拉公式及涉及指数函数和三角函数乘积的基本积分公式。您将学习如何写出一个函数的傅里叶级数，了解奇函数和偶函数在不同背景下的应用，并通过示例解释奇偶函数的不同特点。 课程将详细讲解奇函数和偶函数的傅里叶级数，以及如何在不同区间内计算傅里叶系数。您将掌握利用傅里叶级数解决恒等式的技巧，并简要了解周期函数在评价傅里叶级数中的作用。您还将学习如何评估指数、三角、代数和绝对值函数的傅里叶级数。课程最后将涵盖半范围傅里叶级数，以及如何计算函数的余弦级数和正弦级数。多个问题将逐步解决并详细解释。 课程的最后一个作业将综合所学的所有属性，包括对傅里叶半系列的理解。作为额外内容，您将学习谐波分析及如何计算函数的第一和第二谐波，还将学习不同类型区间的谐波系数计算。此外，课程将介绍傅里叶变换的基本概念，教您如何计算傅里叶正弦变换和余弦变换及其逆变换。您还将学习在解决问题时如何在积分下进行求导的技巧，以及部分导数和链规则相关知识。 让我们开始学习吧！
Welcome to this course on Fourier Series. This is a part of Engineering Maths. I am Suman Mathews, math educator and tutor. I have a double master's in Maths and I have taught Math for three decades to college and High school students. By taking this Course on Fourier Series, you will learn the basics of Analytical Mathematics. In this course, you are introduced to the Euler's formula and basic formulas of integration which involve integrals of the product of the exponential and trigonometric functions. You learn how to write the Fourier series of a function. You learn about odd and even functions in different contexts, not just the traditional definition. Different aspects of odd and even functions are explained with examples.The Fourier series of odd and even functions is explained. You will understand how to calculate the Fourier coefficients in different intervals for different functions. You understand the trick of solving identities using the Fourier series.There is a brief introduction to the role of periodic functions in evaluating the Fourier series.You learn how to evaluate the Fourier series of the exponential, trigonometric, algebraic, modulus functions and more.The course concludes with half range Fourier SeriesYou will also learn how to calculate the cosine series and the sine series of a function. A number of problems are completely solved with steps clearly explained. The last assignment covers all the properties learnt in this course together with an understanding of the Fourier half series.As a bonus, you will learn about Harmonic Analysis and how to calculate the 1st and 2nd harmonic for a function. Also learn how to calculate Harmonic coefficients for different types of intervals.Learn Essential Concepts in Demystifying Fourier Transforms. You'll learn how to calculate Fourier Sine and Cosine Transforms and how to evaluate their Inverse. Also learn the technique of differentiating under the integral while solving problems.Learn about Partial Derivatives and the Chain Rule for Differentiating them.So let's start learning!
